Abstract
In an article in Science on "Bayes' Theorem in the 21st Century", Bradley Efron uses Bayes' theorem to calculate the probability that twins are identical given that the sonogram shows twin boys. He concludes that Bayesian calculations cannot be uncritically accepted when using uninformative priors. While we agree that the choice of the prior is essential, we argue that the calculations on identical twins give a biased impression of the influence of uninformative priors in Bayesian data analyses.
Highlights
While we wholeheartedly agree that statistical results should not be uncritically accepted, we find Efron’s example ineffective in showing that Bayesian statistics require more careful checking than any other kind of statistics
In his example on uninformative priors, Efron uses Bayes’ theorem to calculate the probability that twins are identical given that the sonogram shows twin boys. Efron finds this probability to be 2/3 when using an uninformative prior versus 1/2 with an informative prior and thereby concludes that an uninformative prior does not have the desired neutral effects on the output of Bayes’ rule. We argue that this example is relatively useless in illustrating Bayesian data analysis
We agree with Efron[1] that the choice of the prior is essential, we conclude that his article gives a biased impression of the influence of uninformative priors. In his example using Bayes’ theorem, we found no reliable support for his main conclusion that Bayesian calculations cannot be uncritically accepted when using uninformative priors
Summary
Any reports and responses or comments on the article can be found at the end of the article. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. How to cite this article: Amrhein V, Roth T and Korner-Nievergelt F. We clarified that our approach is different from the calculations provided by Efron. We shortened the manuscript and removed statements that were criticized by referee Michael McCarthy
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
